The statement $(\sim( p \Leftrightarrow \sim q )) \wedge q$ is :
- a tautology
- a contradiction
- equivalent to $(p \Rightarrow q) \wedge q$
- equivalent to $( p \Rightarrow q ) \wedge p$
The Correct Option is D
Solution and Explanation
The correct option is (D): equivalent to $( p \Rightarrow q ) \wedge p$
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Concepts Used:
Validating Statements
To discuss: When a statement is true. To answer this question, one must answer all the following questions. What does the statement mean to say ‘when this statement is true' and 'when this statement is not true? The answer to these questions entirely depends upon which of the special words and phrases “and”, “or”, and which of the implications “if and only”, “if-then”, and which of the quantifiers “there exists”, “for every”, seems in the given statement. Here, we shall be discussing some techniques to find when a statement is valid.
The list of some general rules for checking whether a statement is true or not.
Rule 1 - If p and q are mathematical statements, then in order to show that the statement “p and q” is true, the stated steps should be followed.
Rule 2 - Statements with “Or”.
Rule 3 - Statements with “If-then”.
Rule 4 - Statements with “if and only if ”.